How does vanish gradient restrict RNN to not work for long range dependencies?
Vanishing gradient is: as the gradient starts to flow from the end of the network (right side of the network) to the start of the network (left side of the network), it will be multiplied by numbers less than 1 and gradually it will become weaker and weaker and when it arrives to the first layers, it's so weak that makes almost no change in initial layers parameters.
Now in case of RNNs you can unroll the network, and now you can see that it is like a deep network. For clarity look at the image below (taken from a course by Andrew NG and edited):

Red arrows show the way of gradient backpropagation and you can see that in each step they are multiplied by a number (actually a matrix is multiplied in another matrix). If this number is less than one, then it results in vanishing gradient. If this number is greater than one it will result in exposure (which can be controlled by simply clipping it to a max value). The higher the steps, the more of vanishing or exploding effect.
But they have found a solution for this problem, LSTM or GRU. What these units do is that they will make a highway for gradient to backpropagate through (in each state it will be multiplied by 1). So gradient can travel for longer distance (from French into France). Even though, the problem still exists for very long relations.
If you know what is a ResNet and how it works, you can find the same concept behind LSTM or GRU and ResNets as both make a highway for gradient to flow back.
You can have an intuition of how LSTM or GRU works by following the forward pass and assuming what they are doing as locking the concepts in memory cells. Like when the network sees the word France it will understand that it's an important word and maybe it will become handy later. So it will put the France word in one of it's memory cells and keeps it there for several steps and when it wants to guess the language it will use this memory cell to predict French not English or Persian. Then it can release that memory cell and use this cell for something else.
If you want to learn more and get better intuition, I highly recommend you to look at this link: CS231n of MIT - lecture 10